CN112199818B - A method for calculating armature magnetomotive force of permanent magnet motor using star-delta connection - Google Patents

Abstract

The invention discloses an armature magnetomotive force calculation method of a permanent magnet motor adopting a star-delta connection method, which relates to the field of armature magnetomotive force calculation of fractional slot permanent magnet motors and comprises the following steps: dividing the single-phase armature winding into a star-shaped part winding and a triangular part winding; the calculating step comprises: the calculation parts comprise calculation parts such as star-shaped part winding magnetomotive force calculation, triangle-shaped part winding magnetomotive force calculation, single-phase forward synthetic magnetomotive force calculation, single-phase reverse synthetic magnetomotive force calculation and the like. The calculation method is provided for solving the problem that the armature magnetomotive force of the multilayer winding fractional slot permanent magnet motor adopting the star-delta connection method is difficult to calculate under any number of turns and mechanical angle difference, and the calculation problem of the armature magnetomotive force of the multilayer winding armature adopting the star-delta connection method is solved. The method can accurately calculate the armature magnetomotive force of the multi-layer winding fractional slot permanent magnet motor adopting the star-delta connection method, provides an effective armature magnetomotive force calculation method for the permanent magnet motor, and can be further used for other analyses of the permanent magnet motor.

Description

A method for calculating armature magnetomotive force of permanent magnet motor using star-delta connection

technical field

The invention relates to the field of fractional slot permanent magnet motors, in particular to a method for calculating armature magnetomotive force of permanent magnet motors using star-delta connection.

Background technique

Compared with traditional integer-slot permanent magnet motors, fractional-slot permanent magnet motors have large torque, high power density, small size, and high efficiency and utilization rate, and have been widely used in electric vehicles, wind power generation, aerospace and other fields. Due to the current distribution in the windings of the fractional-slot permanent magnet motor, the armature magnetomotive force contains high-amplitude low-order harmonics. These harmonics run asynchronously in the iron core and permanent magnet, resulting in eddy current losses in the iron core and permanent magnet. The motor produces effects such as noise and vibration, which reduces the operating efficiency of the permanent magnet motor. It may even cause the permanent magnet to overheat and cause irreversible demagnetization and abnormal operation of the permanent magnet motor, which may cause potential safety hazards during use.

In order to solve the above problems, scholars at home and abroad have carried out extensive research. At present, scholars have done many researches on how to eliminate the high-amplitude low-order harmonics in fractional-slot concentrated-winding permanent magnet motors. For example, the phase shift of the winding current is studied, and multiple three-phase currents are introduced to make it select the appropriate phase shift in space and time to reduce or eliminate the harmonics of the armature magnetomotive force. By using coils with a different number of turns on each side and using flux barriers at specific locations in the stator core, asymmetrical turns and a winding structure across two pitches, this approach results in a reduction in output torque. The fractional slot permanent magnet motor winding adopts the star-delta connection method, which has attracted the attention of scholars because of its simple manufacturing process and easy implementation. This method only changes the connection of the stator windings of the fractional-slot permanent magnet motor. Practice shows that this new winding connection is very effective in eliminating the harmonics of the armature magnetomotive force. However, neither the calculation of the armature magnetomotive force harmonics of the star-delta winding nor the analysis of the offset angle of the multi-layer winding has been systematically studied, so how to optimize the winding parameters to better reduce the armature magnetomotive force There are still deficiencies in potential harmonics.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is to overcome the deficiencies of the prior art and provide a method for calculating armature magnetomotive force using a star-delta connection permanent magnet motor. The stator winding fractional slot permanent magnet motor with a fixed turns ratio and a different mechanical angle can suppress the low-order harmonics of the armature magnetomotive force, thereby suppressing the eddy current loss in the iron core and the permanent magnet, and avoiding the irreversible damage caused by the overheating of the permanent magnet. Demagnetization phenomenon, improve the efficiency of permanent magnet motor, increase the safety of motor use.

The present invention adopts the following technical solutions for solving the above-mentioned technical problems:

A method for calculating armature magnetomotive force of a permanent magnet motor with star-delta connection proposed according to the present invention includes the following steps:

Step 1. For the multi-layer winding fractional slot permanent magnet motor using the star-delta connection method, the armature winding of each phase is divided into a star part winding and a delta part winding;

Step 2. Take the total number of turns of the single-phase armature winding as N _s =N _Y +N _Δ , where N _Y and N _Δ are the number of turns of the star partial winding and the delta partial winding, respectively, and the proportional coefficient of the star partial winding and the delta partial winding N _Y ', N _Δ ' are respectively:

Step 3. According to Kirchhoff's current law, the relationship between the current I _iY of the ith phase star part and the current I _iΔ of the ith phase triangle part is:

In the formula, m is the phase number of the permanent magnet motor, i is the specific phase number, i=1, 2, 3..., the phase of the winding current of the star part is ahead of the phase π/2m electrical angle of the current of the winding current of the delta part of the same phase;

Step 4. Combine the phase and amplitude relationship of the armature winding current in the star-delta connection method, and perform Fourier decomposition on the square wave magnetomotive force of the star partial winding and the delta partial winding to obtain an m-phase fractional slot permanent magnet motor The armature magnetomotive force F _Yv-m of the star part winding is:

The delta partial winding armature magnetomotive force F _Δv-m is:

In the formula, v is the armature magnetomotive force harmonic order, t is the time, ω is the angular frequency of the current, I is the effective value of the sinusoidal current, Z ₀ is the number of stator slots of the unit motor, and k _NvYl is the permanent magnet motor stator winding is the star-shaped partial harmonic winding coefficient when the layer is l, k _NvΔl is the triangular partial harmonic winding coefficient when the stator winding of the permanent magnet motor is l-layer, α is the mechanical angle of the permanent magnet motor, α _s is the star-shaped partial winding and the triangular part Winding difference mechanical angle;

Step 5. If the phasors of the armature magnetomotive force of the star part winding and the delta part winding are in the same direction, synthesize the armature magnetomotive force of the star part winding and the delta part winding to obtain the single-phase forward synthetic armature magnetomotive force F _tv-m is:

为m相永磁电机三角形部分绕组电枢磁动势偏移角度；Among them, h _t-YΔm is the forward synthesis factor of the armature magnetomotive force of the star-delta part winding in the m-phase permanent magnet motor,

is the armature magnetomotive force offset angle of the triangular part winding of the m-phase permanent magnet motor;

Step 6. If the armature magnetomotive force phasors of the star-shaped partial winding and the delta partial winding are in opposite directions, the single-phase reverse synthetic magnetomotive force F _tv-m ' is obtained as:

In the formula, h _t-YΔm ' is the reverse synthesis factor of the armature magnetomotive force of the star-delta partial winding in the m-phase permanent magnet motor.

As a further optimization scheme of the armature magnetomotive force calculation method of the star-delta connection permanent magnet motor according to the present invention,

As a further optimization scheme of the armature magnetomotive force calculation method of the star-delta connection permanent magnet motor according to the present invention,

As a further optimization scheme of the armature magnetomotive force calculation method of the star-delta connection permanent magnet motor according to the present invention,

As a further optimization scheme of the armature magnetomotive force calculation method of the permanent magnet motor using the star-delta connection method of the present invention, for the star partial winding and the delta partial winding with a given winding turns ratio and mechanical angle difference For the fractional slot permanent magnet motor, the steps of unidirectionally synthesizing the magnetomotive force F _tv-m ' are as follows:

Step (1), keep the star partial winding and the delta partial winding evenly distributed in different sectors of each phase, that is, the star partial harmonic winding coefficient is the same as the delta partial harmonic winding coefficient;

k _NvYl =k _NvΔl ;

Among them, l=2k, k=1, 2, 3..., l is the number of PM motor winding layers, k _NvYl is the star-shaped partial harmonic winding coefficient when the permanent magnet motor stator winding is l-layer, and k _NvΔl is the PM motor When the stator winding is l-layer, the triangular partial harmonic winding coefficient;

Step (2), keep the magnetomotive force amplitudes of the star part winding and the delta part winding consistent, and only consider the situation where the armature magnetomotive force phasor directions of the star part winding and the delta part winding are opposite;

为星形部分绕组电流，

为三角形部分绕组电流；In the formula,

is the winding current of the star part,

is the winding current of the delta part;

Step (3), for the m-phase four-layer winding fractional slot permanent magnet motor, the first sector is a star partial winding, and the second sector is a delta partial winding; the phase difference of the current in the star partial winding and the delta partial winding is used is π/2m, the mechanical angle of the star-delta winding phase difference is determined by the offset angle α _p of the second sector

In the formula, α ₀ is the slot pitch angle of the fractional slot permanent magnet motor;

Step (4), when the number of stator slots of the unit motor in the m-phase four-layer winding fractional slot permanent magnet motor is Z ₀ =4mk, the low-order armature magnetomotive force can be suppressed, and the single-phase reverse synthetic magnetomotive force F _{tv- m} ' is:

Among them, k _NvY4 is the harmonic winding coefficient of the star part and the triangle part when the permanent magnet motor winding is four layers.

Compared with the prior art, the present invention adopts the above technical scheme, and has the following technical effects:

The calculation method proposed by the invention solves the calculation problem of the armature magnetomotive force of any m-phase fractional slot permanent magnet motor with an even number of stator layers for any number of turns and a mechanical angle difference; The stator winding fractional slot permanent magnet motor with the highest turns ratio and different mechanical angles can suppress the low-order harmonics of the armature magnetomotive force, thereby suppressing the eddy current loss in the iron core and the permanent magnet, and avoiding the irreversible demagnetization caused by the overheating of the permanent magnet. phenomenon, improve the efficiency of permanent magnet motor use, and increase the safety of motor use.

Description of drawings

FIG. 1 is a schematic diagram of the winding connection method of the multi-layer winding fractional slot permanent magnet motor using the star-delta connection method described in the present invention.

FIG. 2 is a schematic diagram of the current phase and amplitude in the winding of the fractional slot permanent magnet motor using the star-delta connection method in FIG. 1 .

Figure 3 is a schematic diagram of the armature magnetomotive force in the winding of the fractional slot permanent magnet motor using the star-delta connection method in Figure 1; wherein, (a) is the armature magnetomotive force when k=1, (b) is k=3 When the armature magnetomotive force.

Figure 4 is a schematic diagram of a fractional-slot permanent magnet motor with four different winding structures; among them, (a) is a Y-Y connection double-winding permanent magnet motor, (b) is a Y-Δ connection double-winding permanent magnet motor, (c) ) is a four-layer winding permanent magnet motor with Y-Y connection, and (d) is a double-winding permanent magnet motor with Y-Δ connection.

Figure 5 is a schematic diagram of the armature magnetomotive force of the fractional slot permanent magnet motor with different winding structures in Figure 4; wherein, (a) is the armature magnetomotive force of the Y-Y connection double-layer winding permanent magnet motor, and (b) is the Y- The armature magnetomotive force of the double-layer winding permanent magnet motor with Δ connection method, (c) is the armature magnetomotive force of the four-layer winding permanent magnet motor with Y-Y connection method, and (d) is the magnetomotive force of the four-layer winding permanent magnet motor with Y-Δ connection method. Pivot magnetomotive force.

Detailed ways

Below in conjunction with accompanying drawing, the technical scheme of the present invention is described in further detail:

The embodiment described in the present invention is only for the fractional slot permanent magnet motor with multi-layer winding in star-delta connection, and the present invention can also be applied to other arbitrary turns ratio and offset angle multi-layered motor in star-delta connection. Windings in fractional slot permanent magnet motors.

Example 1

For the m-phase fractional slot permanent magnet motor with multi-layer windings in star-delta connection, the armature windings of each phase are divided into star-shaped partial armature windings and delta-shaped partial armature windings, as shown in Figure 1.

In order to simplify the calculation, the total number of turns of the single-phase armature winding is taken as N _s =N _Y +N _Δ , and the proportional coefficient of the star part winding and the delta part winding is:

According to Kirchhoff's current law, the relationship between the star winding current I _iY and the delta winding current I _iΔ is:

In the formula, i is the specific phase number (i=1, 2, 3...), the phase of the star winding current is ahead of the phase π/2m electrical angle of the in-phase delta winding current, and the specific current phase and amplitude relationship is shown in the figure 2 shown.

The square wave magnetomotive force of the star partial winding and the delta partial winding is decomposed by Fourier, and the armature magnetomotive force of the star partial winding can be obtained as:

The armature magnetomotive force of the delta winding is:

In the formula, v is the armature magnetomotive force harmonic order, t is the time, ω is the angular frequency of the current, I is the effective value of the sinusoidal current, Z ₀ is the number of stator slots of the unit motor, and k _NvYl is the permanent magnet motor stator winding is the star-shaped partial harmonic winding coefficient when the layer is l, k _NvΔl is the triangular partial harmonic winding coefficient when the stator winding of the permanent magnet motor is l-layer, α is the mechanical angle of the permanent magnet motor, α _s is the star-shaped partial winding and the triangular part Winding difference mechanical angle;

If the phasors of the armature magnetomotive force of the star part winding and the delta part winding are in the same direction, and the armature magnetomotive force of the star part winding and the delta part winding are synthesized, the single-phase forward combined armature magnetomotive force can be obtained as:

In the formula, h _t-YΔm is the forward synthesis factor of the armature magnetomotive force of the star-delta partial winding in the m-phase permanent magnet motor

为m相永磁电机三角形部分绕组电枢磁动势偏移角度in,

is the offset angle of the armature magnetomotive force of the delta winding of the m-phase permanent magnet motor

If the phasors of the armature magnetomotive force of the star part winding and the delta part winding are opposite in direction, the single-phase reverse combined magnetomotive force can be obtained as:

In the formula, h _t-YΔm ' is the reverse synthesis factor of the armature magnetomotive force of the star-delta partial winding in the m-phase permanent magnet motor

The steps for suppressing the harmonic components of low-order magnetomotive force at a given turn ratio and mechanical angle of the star-shaped partial winding and the delta-shaped partial winding are as follows:

Keep the star partial winding and the delta partial winding evenly distributed in different sectors of each phase, that is, the star partial harmonic winding coefficient is the same as the delta partial harmonic winding coefficient

k _NvYl =k _NvΔl

Among them, l=2k, k=1, 2, 3..., l is the number of PM motor winding layers, k _NvYl is the star-shaped partial harmonic winding coefficient when the permanent magnet motor stator winding is l-layer, and k _NvΔl is the PM motor When the stator winding is l-layer, the triangular partial harmonic winding coefficient;

Keep the magnetomotive force amplitudes of the star partial winding and the delta partial winding consistent, and only consider the situation where the armature magnetomotive force phasors of the star partial winding and the delta partial winding are in opposite directions

For the m-phase four-layer winding fractional slot permanent magnet motor, the first sector is a star partial winding, and the second sector is a delta winding. The phase difference of the current in the star partial winding and the delta partial winding is π/2m, and the mechanical angle of the star-delta partial winding difference is determined by the second sector offset angle α _p

When the number of stator slots of the unit motor in the m-phase four-layer winding fractional-slot permanent magnet motor is Z ₀ =4mk, the low-order armature magnetomotive force can be suppressed. The armature magnetomotive force of the fractional slot permanent magnet motor with different stator slots is as follows As shown in Figure 3, (a) in Figure 3 is the armature magnetomotive force when k=1, and (b) in Figure 3 is the armature magnetomotive force when k=3; single-phase armature magnetomotive force for

Among them, k _NvY4 is the harmonic winding coefficient of the star part and the triangle part when the permanent magnet motor winding is four layers.

In this embodiment, in order to compare the suppression effect of the fractional slot permanent magnet motor with a given star-delta connection on the harmonics of the low-order armature magnetomotive force, the star-star connection and the star-delta connection will be used. The armature magnetomotive force of the 10-pole 12-slot fractional-slot permanent magnet motor with different winding layers is simulated. Assuming that all designed rotor sizes, permanent magnet sizes, magnetization methods, arrangement methods, and copper volumes are the same, Figure 4 shows four fractional-slot permanent magnet motors with different winding structures, and (a) in Figure 4 is Y-Y Connection double-layer winding permanent magnet motor, (b) in Figure 4 is a Y-Δ connection double-layer winding permanent magnet motor, Figure 4 (c) is a Y-Y connection four-layer winding permanent magnet motor, in Figure 4 (d) is a Y-Δ connection double-winding permanent magnet motor. The fractional slot permanent magnet motor with four different winding structures has a stator slot number Z of 12 and a rotor pole pair number p of 5. Table 1 shows the same basic parameters of the four fractional slot permanent magnet motors.

Table 1

If the number of stator slots of the unit motor of the three-phase multi-layer winding fractional-slot permanent magnet motor is 12, the single-phase armature magnetomotive force of the fractional-slot permanent magnet motor is:

In this embodiment, the corresponding armature magnetomotive force of the fractional-slot permanent magnet motor with four different winding structures is shown in Figure 5, and (a) in Figure 5 is the armature magnetomotive force of the Y-Y connection double-layer winding permanent magnet motor. (b) in Figure 5 is the armature magnetomotive force of the Y-Δ connection double-layer winding permanent magnet motor, and (c) in Figure 5 is the armature magnetomotive force of the four-layer winding permanent magnet motor with Y-Y connection, (d) in Fig. 5 is the magnetomotive force of the armature of the four-layer winding permanent magnet motor with Y-Δ connection. Perform Fourier decomposition on the armature magnetomotive force of the obtained different winding structures, and the harmonic amplitudes of each order can be obtained as shown in Table 2.

Table 2 Amplitude percentage of each harmonic order of different winding structures in Example 1

Corresponding to Table 2, it can be seen that the multi-layer winding three-phase permanent magnet motor with star-delta connection can completely eliminate the armature harmonic magnetomotive force with harmonic orders of v=1, 11, 13, 23, 26, etc. It is proved that The fractional slot permanent magnet motor winding adopts the star-delta connection method to suppress the low-order harmonics, which can effectively reduce the iron core loss of the permanent magnet motor and the rotor and the eddy current loss of the permanent magnet, improve the use efficiency of the permanent magnet motor, and increase the use of the motor. safety.

Centering on the embodiments of the present invention, the specific calculation process of the method is described in detail here. The described calculation process or the specific embodiment of some features should be understood that this specification is only for describing the present invention with respect to the motor structure of the given embodiment. In fact, for fractional slot permanent magnet motor armature magnetomotive force of different winding structures Certain details may vary during the analysis, and these variations should fall within the scope of the present invention.

Those skilled in the art can understand that the accompanying drawing is only a schematic diagram of a preferred embodiment, and the above embodiments of the present invention are only for description, and do not represent the advantages or disadvantages of the embodiments. The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included in the protection of the present invention. within the range.

Claims (5)

1. a method for calculating armature magnetomotive force using star-delta connection permanent magnet motor, is characterized in that, comprises the following steps: Step 1. For the multi-layer winding fractional slot permanent magnet motor using the star-delta connection method, the armature winding of each phase is divided into a star part winding and a delta part winding; Step 2. Take the total number of turns of the single-phase armature winding as N _s =N _Y +N _Δ , where N _Y and N _Δ are the number of turns of the star partial winding and the delta partial winding, respectively, and the proportional coefficient of the star partial winding and the delta partial winding N _Y ', N _Δ ' are respectively:

Step 3. According to Kirchhoff's current law, the relationship between the current I _iY of the ith phase star part and the current I _iΔ of the ith phase triangle part is:

In the formula, m is the phase number of the permanent magnet motor, i is the specific phase number, i=1, 2, 3..., the phase of the winding current of the star part is ahead of the phase π/2m electrical angle of the current of the winding current of the delta part of the same phase; Step 4. Combine the phase and amplitude relationship of the armature winding current in the star-delta connection method, and perform Fourier decomposition on the square wave magnetomotive force of the star partial winding and the delta partial winding to obtain an m-phase fractional slot permanent magnet motor The armature magnetomotive force F _Yv-m of the star part winding is:

The delta partial winding armature magnetomotive force F _Δv-m is:

In the formula, v is the armature magnetomotive force harmonic order, t is the time, ω is the angular frequency of the current, I is the effective value of the sinusoidal current, Z ₀ is the number of stator slots of the unit motor, and k _NvYl is the permanent magnet motor stator winding is the star-shaped partial harmonic winding coefficient when the layer is l, k _NvΔl is the triangular partial harmonic winding coefficient when the stator winding of the permanent magnet motor is l-layer, α is the mechanical angle of the permanent magnet motor, α _s is the star-shaped partial winding and the triangular part Winding difference mechanical angle; Step 5. If the phasors of the armature magnetomotive force of the star part winding and the delta part winding are in the same direction, synthesize the armature magnetomotive force of the star part winding and the delta part winding to obtain the single-phase forward synthetic armature magnetomotive force F _tv-m is:

Among them, h _t-YΔm is the forward synthesis factor of the armature magnetomotive force of the star-delta part winding in the m-phase permanent magnet motor,

is the armature magnetomotive force offset angle of the triangular part winding of the m-phase permanent magnet motor; Step 6. If the armature magnetomotive force phasors of the star-shaped partial winding and the delta partial winding are in opposite directions, the single-phase reverse synthetic magnetomotive force F _tv-m ' is obtained as:

In the formula, h _t-YΔm ' is the reverse synthesis factor of the armature magnetomotive force of the star-delta partial winding in the m-phase permanent magnet motor. 2. a kind of armature magnetomotive force calculation method adopting star-delta connection permanent magnet motor according to claim 1, is characterized in that,

3. a kind of armature magnetomotive force calculation method adopting star-delta connection permanent magnet motor according to claim 1, is characterized in that,

4. a kind of armature magnetomotive force calculation method using star-delta connection permanent magnet motor according to claim 1, is characterized in that,

5. a kind of armature magnetomotive force calculation method adopting star-delta connection permanent magnet motor according to claim 1, is characterized in that, for adopting the star-shaped partial winding of given winding turns ratio, mechanical angle difference And the fractional-slot permanent magnet motor with delta partial winding, the steps of uniphase reverse synthesis of magnetomotive force F _tv-m ' are as follows: Step (1), keep the star partial winding and the delta partial winding evenly distributed in different sectors of each phase, that is, the star partial harmonic winding coefficient is the same as the delta partial harmonic winding coefficient; k _NvYl =k _NvΔl ; Among them, l=2k, k=1, 2, 3..., l is the number of PM motor winding layers, k _NvYl is the star-shaped partial harmonic winding coefficient when the permanent magnet motor stator winding is l-layer, and k _NvΔl is the PM motor When the stator winding is l-layer, the triangular partial harmonic winding coefficient; Step (2), keep the magnetomotive force amplitudes of the star part winding and the delta part winding consistent, and only consider the situation where the armature magnetomotive force phasor directions of the star part winding and the delta part winding are opposite;

In the formula,

is the winding current of the star part,

is the winding current of the delta part; Step (3), for the m-phase four-layer winding fractional slot permanent magnet motor, the first sector is a star partial winding, and the second sector is a delta partial winding; the phase difference of the current in the star partial winding and the delta partial winding is used is π/2m, the mechanical angle of the star-delta winding phase difference is determined by the offset angle α _p of the second sector

In the formula, α ₀ is the slot pitch angle of the fractional slot permanent magnet motor; Step (4), when the number of stator slots of the unit motor in the m-phase four-layer winding fractional slot permanent magnet motor is Z ₀ =4mk, the low-order armature magnetomotive force can be suppressed, and the single-phase reverse synthetic magnetomotive force F _{tv- m} ' is:

Among them, k _NvY4 is the harmonic winding coefficient of the star part and the triangle part when the permanent magnet motor winding is four layers.

Images